Abstract

Monte-Carlo evaluation of path integrals is a ubiquitous method to study a wide range of strongly interacting systems, from nuclear to condensed matter physics. For many interesting problems, such as finite density systems and real-time evolution, however, its applicability is severely limited due to the infamous sign problem which arises when the path integral measure has a fast oscillating phase. In this talk, I will discuss a class of approaches to mitigate the sign problem based on the application of Picard-Leschetz theory to path integrals. These approaches stem from the idea of deforming the domain of path integration in complex field space in a way that preserves the path integral but ameliorates the phase oscillations. I will discuss various implementations of this idea in Monte-Carlo algorithms with several examples.